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Definitions. Given sets. Given sets : examples. To introduce declaration of a set of student ; [ student ] In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]. Declaration of variables.

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Definitions

Definitions


Given sets

Given sets


Given sets examples

Given sets : examples

  • To introduce declaration of a set of student ; [ student ]

  • In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]


Declaration of variables

Declaration of variables

  • A name is assigned a type when it is declared. Once a given set is declared, we can declare variables.

  • Example

    stud1 : Student --- declaring a student

    library1 : pBook --- declaring a set of books

    primes : p  --- declaring primes to be a set of integers

    newestbook : Book   --- what the book is and a number

    showing the copy

    library : p(Book   ) --- declaring a library as a set of copies of

    books


Abbreviations

Abbreviations

  • Syntactic equivalence

  • Example

    basic_ref == {math, intro_to_computers}

  • Is equivalent to the declaration basic_ref : p Book together with

    the predicate basic_ref = {math, intro_to_computers}


Enumerated types

Enumerated types

  • Use data type definition to introduce a type with a small number of members

  • Name ::= list of elements separated by |

  • Example

    YesNo ::= yes | no


Axiomatic description

Axiomatic description

  • To introduce variables along with predicates giving further information


Consistency

Consistency


Consistency1

Consistency


Consistency example

Consistency : example


Generic definitions

Generic Definitions


Generic abbreviations

Generic Abbreviations


Generic axiomatic definitions

Generic Axiomatic Definitions


Generic axiomatic definitions1

Generic Axiomatic Definitions


Generic axiomatic definitions2

Generic Axiomatic Definitions


Generic axiomatic definitions3

Generic Axiomatic Definitions


Characteristic set

Characteristic set


Characteristic set1

Characteristic set


Characteristic set2

Characteristic set


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